We showed that, as we add more Gaussian variables, the capacity of the system decreases and retrieval is harder to achieve because the basin of attraction of the memory states is becoming smaller if we are at a sufficiently high memory loading. This is a consequence of the spherical symmetry brought in by the Gaussian parts of the memories, as discussed in Sec. . When all the variables of the patterns are Gaussian the only way we can have retrieval is when the number of the patterns is of \(O(1)\)  because, here, the local field has finite variance. In any case, when the memories are present in an extensive number, the Gaussian overlap of the condensed patterns works as a spin glass noise added to that of the non condensed ones. The result is that, as we have demonstrated both numerically and theoretically, the capacity drops quadratically as \(1-p\)  at zero temperature, while at \(T>0\)  the spinodal lines, as well as the first order transition lines, are a combination of \((1-p)^2\)  and \((1-p)^4\)  terms. Consequently, the lines get squeezed towards the vertical line \(\alpha =0\)  when approaching the purely Gaussian model, but at the same time the critical point at \(T_g=1\)  remains unchanged and this could bring us to the next challenge concerning the behavior of the system when the number of memories is of \(O(N^\delta )\)  with \(\delta <1\) . This could be particularly interesting for developing the proper theoretical framework to experiments in [1]}.
